In wireless systems such as multiple-input, multiple-output (MIMO) systems, to achieve the full benefit of transmitter processing and for optimal beamforming, the transmitter device, such as an enhanced Node B (eNB) in Long Term Evolution (LTE) systems, needs to have knowledge of the downlink (DL) channel. In time-division duplex (TDD) systems, such knowledge at the transmitter may be obtained by using downlink-uplink (DL-UL) channel reciprocity and transmitting reference signals such as pilot signals from the receiver user equipment (UE) to the transmitter eNB. However, in general, the UE has to measure the DL instantaneous channel on a DL reference signal and feed it back to the eNB. Feeding back the full channel may incur significant overhead. As a result, limited feedback schemes are employed in MIMO systems.
Some MIMO systems may employ a fixed codebook approach in which a codebook is constructed using a particular criterion. For example, in independent and identically distributed (IID) channels, the Grassmannian line packing technique may be utilized such that the distance between any two codewords is maximized. In the presence of correlation, there are other alternatives to codebook construction. Such fixed codebooks are particularly useful for channels which do not undergo rapid changes in their statistical properties. However, the design approaches may be complicated.
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